Differentiable Energy-Based Regularization in GANs: A Simulator-Based Exploration of VQE-Inspired Auxiliary Losses

This paper presents an exploratory, simulator-based proof of concept investigating whether differentiable energy terms derived from parameterized quantum circuits can serve as auxiliary regularization signals in Generative Adversarial Networks (GANs). We augment the Auxiliary Classifier GAN (ACGAN) generator objective with a Variational Quantum Eigensolver (VQE)-inspired energy term computed from class-specific Ising Hamiltonians using Qiskit's EstimatorQNN and TorchConnector. All experiments are performed on a noiseless statevector simulator with only four qubits, using a deliberately simple Hamiltonian parameterization. On MNIST, the energy-regularized model initially achieves high external-classifier accuracy (99-100 percent) within five epochs compared to 87.8 percent for an earlier, unmatched ACGAN baseline. However, a rigorous, pre-registered ablation study demonstrates that these improvements are fully replicated by simple classical alternatives, including learned per-class biases, MLP-based surrogates, random noise, and even an unregularized baseline under matched training conditions. All classical variants reach approximately 99 percent accuracy. For sample quality as measured by FID, classical baselines are not merely equivalent but systematically superior to the VQE-based formulation. We therefore report a clear negative result. The VQE-inspired energy term provides no measurable causal benefit beyond trivial classical regularizers in this setting. The primary contribution of this work is methodological, demonstrating both the technical feasibility of differentiable VQE integration into GAN training and the necessity of rigorous ablation studies to avoid spurious claims of quantum-enhanced performance.